A preliminary analysis of low frequency pressure oscillations in hybrid rocket motors

Past research with hybrid rockets has suggested that certain motor operating conditions are conducive to the formation of pressure oscillations, or flow instabilities, within the motor combustion chamber. These combustion-related vibrations or pressure oscillations may be encountered in virtually any type of rocket motor and typically fall into three frequency ranges: low frequency oscillations (0-300 Hz); intermediate frequency oscillations (400-1000 Hz); and high frequency oscillations (greater than 1000 Hz). In general, combustion instability is characterized by organized pressure oscillations occurring at well-defined intervals with pressure peaks that may maintain themselves, grow, or die out. Usually, such peaks exceed +/- 5% of the mean chamber pressure. For hybrid motors, these oscillations have been observed to grow to a limiting amplitude which may be dependent on factors such as fuel characteristics, oxidizer injector characteristics, average chamber pressure, oxidizer mass flux, combustion chamber length, and grain geometry. The approach taken in the present analysis is to develop a modified chamber length, L, instability theory which accounts for the relationship between pressure and oxidizer to fuel concentration ratio in the motor.